A real harmonizable \(S\alpha S\)  process is stationary if and only if \(M\)  is isotropic, i.e. its spectral measure is of the form \(k=m\cdot \gamma \)  [1]}.
In this case \(X\)  is called a stationary real harmonizable \(S\alpha S\)  process.
Furthermore, by [1]} the finite-dimensional characteristic function of a SRH \(S\alpha S\)  process \(X\)  is given by
\(\mathbb {E}\left[\exp \left\lbrace i\sum _{i=1}^ns_iX(t_i)\right\rbrace \right]=\exp \left\lbrace -\lambda _\alpha \int _\mathbb {R}\left|\sum _{j,k=1}^ns_js_k\cos \left(\left(t_k-t_j\right)x\right)\right|^{\alpha /2}m(dx)\right\rbrace \) 
